The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A141402 Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows. 1

%I #7 Mar 31 2021 01:28:02

%S 0,1,1,4,8,4,9,25,25,9,16,52,80,52,16,25,89,169,169,89,25,36,136,292,

%T 360,292,136,36,49,193,449,625,625,449,193,49,64,260,640,964,1088,964,

%U 640,260,64,81,337,865,1377,1681,1681,1377,865,337,81,100,424,1124,1864,2404,2600,2404,1864,1124,424,100

%N Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows.

%H G. C. Greubel, <a href="/A141402/b141402.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = n^2 + (2*k*(n-k))^2.

%F Sum_{k=0..n} T(n, k) = n*(2*n^4 + 15*n^2 + 15*n -2)/15. - _G. C. Greubel_, Mar 30 2021

%e Triangle begins as:

%e 0;

%e 1, 1;

%e 4, 8, 4;

%e 9, 25, 25, 9;

%e 16, 52, 80, 52, 16;

%e 25, 89, 169, 169, 89, 25;

%e 36, 136, 292, 360, 292, 136, 36;

%e 49, 193, 449, 625, 625, 449, 193, 49;

%e 64, 260, 640, 964, 1088, 964, 640, 260, 64;

%e 81, 337, 865, 1377, 1681, 1681, 1377, 865, 337, 81;

%e 100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100;

%p A141402:= (n,k)-> n^2 + (2*k*(n-k))^2;

%p seq(seq(A141402(n,k), k=0..n), n=0..12); # _G. C. Greubel_, Mar 30 2021

%t T[n_, k_]:= n^2 + (2*k*(n-k))^2;

%t Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

%o (Magma) [n^2 + (2*k*(n-k))^2: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 30 2021

%o (Sage) flatten([[n^2 + (2*k*(n-k))^2 for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 30 2021

%K nonn,easy,tabl

%O 0,4

%A _Roger L. Bagula_, Aug 03 2008

%E Edited by _G. C. Greubel_, Mar 30 2021

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 18 03:12 EDT 2024. Contains 372617 sequences. (Running on oeis4.)